A critical reexamination of default logic, autoepistemic logic, and only knowing

2005 ◽  
pp. 43-60 ◽  
Author(s):  
Joseph Y. Halpern
Keyword(s):  
Default Logic ◽  
Autoepistemic Logic

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming

2021 ◽  
Author(s):  
Jesse Heyninck ◽  
Ofer Arieli
Keyword(s):  
Logic Programming ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Autoepistemic Logic ◽  
Algebraic Framework ◽  
Nonmonotonic Logics

Approximation fixpoint theory (AFT) constitutes an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

scholarly journals Knowledge compilation of logic programs using approximation fixpoint theory

2015 ◽  
Vol 15 (4-5) ◽  
pp. 464-480 ◽  
Author(s):  
BART BOGAERTS ◽  
GUY VAN DEN BROECK
Keyword(s):  
Propositional Logic ◽  
Default Logic ◽  
Knowledge Compilation ◽  
Auxiliary Variables ◽  
Logic Programs ◽  
Autoepistemic Logic ◽  
Recent Advances ◽  
Logical Equivalence ◽  
General Logic

AbstractRecent advances in knowledge compilation introduced techniques to compilepositivelogic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited tonegation-freeprograms. In this paper, we show how to extend it to general logic programs under the well-founded semantics.We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks.

scholarly journals Reasoning about Minimal Belief and Negation as Failure

1999 ◽  
Vol 11 ◽  
pp. 277-300 ◽  
Author(s):  
R. Rosati
Keyword(s):  
Logic Programming ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Polynomial Hierarchy ◽  
Autoepistemic Logic ◽  
The Third ◽  
Negation As Failure ◽  
Negative Introspection

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.

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